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Pedal circle related

Source: 2020 China Southeast 10.6/11.6

August 7, 2020
geometryIsogonal conjugate

Problem Statement

In a quadrilateral ABCDABCD, ∠ABC=∠ADC<90∘\angle ABC=\angle ADC <90^{\circ}. The circle with diameter ACAC intersects BCBC and CDCD again at E,FE,F, respectively. MM is the midpoint of BDBD, and AN⊥BDAN \perp BD at NN. Prove that M,N,E,FM,N,E,F is concyclic.
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